Measurement Invariance

Alignment

• Marsh, H. W., Guo, J., Nagengast, B., Parker, P. D., Asparouhov, T., Muthén, B., & Dicke, T. (2016, accepted). What to do when scalar invariance fails: The extended alignment method for multigroup factor analysis comparison of latent means across many groups. Structural Equation Modeling: A Multidisciplinary Journal.
  
  
• Muthén, B. & Asparouhov, T. (2016). Recent methods for the study of measurement invariance with many groups: Alignment and random effects. Download Mplus files.
  
  
• Asparouhov T. & Muthén, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21:4, 495-508. Download Mplus files.
  
  
• Muthén, B. & Asparouhov T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, Volume 5, DOI: 10.3389/fpsyg.2014.00978
  
  
• Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54:4, 557-585.
  
  

BSEM

• Muthén, B. & Asparouhov, T. (2013). BSEM measurement invariance analysis.
  
  
• Muthén, B. & Asparouhov, T. (2012). Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17, 313-335. Download the 2nd version dated April 14, 2011. View the seven web tables referred to in the paper. View Mplus inputs, data, and outputs used in this version of paper. Download the 1st version dated September 29, 2010 containing a MIMIC section and more tables. Download the corresponding Mplus inputs, data, and outputs. The seven web tables correspond to tables 8, 10, 17, 18, 19, 20, and 21 of the first version.
  
  

Measurement Invariance in EFA

• Asparouhov, T. & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397-438.
  
  

Random Loadings

• Asparouhov, T. & Muthén, B. (2015). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. In Harring, J. R., & Stapleton, L. M., & Beretvas, S. N. (Eds.), Advances in multilevel modeling for educational research: Addressing practical issues found in real-world applications. Charlotte, NC: Information Age Publishing, Inc. Mplus scripts.
  
  

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